Relations on a set.

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We look at the general notion of a relation on a set and give several examples.
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Опубликовано:

3 мар 2021

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Комментарии : 32

@MichaelPennMath 3 года назад

Hey everyone! Here is another video that was accidentally set as unlisted for too long.

@foreachepsilon 3 года назад

“Is friends with” is a common non-transitive relation.

@tdchayes 3 года назад

Hopefully you are friends with yourself (reflexivity), and your friend is friends with you (symmetry), but you might not be friends with your friend's friend! (no transitivity) A great example.

@ulysses_grant 3 года назад

@@tdchayes lol, good one!

@oder4876 3 года назад

Maybe, Actualy i don't know.

@matekon2 3 года назад

A non-transitive relation that has some meaning to it would be the relation of "incrementation". For numbers, it would be aRb iff b=a+1. I could also think of an analogue of this relation for sets (ARB iff A subset of B and |A|+1=|B)|. In a data structure like a heap, the relation of "parent" if not transitive. In fact, so is the relation of "parents" in real life.

@chasereiter4760 3 года назад

At 4:22, another possible relation could be "less than or equal to." This makes sense since for all x and y such that x | y, then x

@oida10000 3 года назад

A non-transitiv, non-reflexive but symetric realtion would the is-co-prime-to-relation.

@tomatrix7525 3 года назад

Nice

@mithutamang3888 2 года назад

Symmetry is satisfied by this non-strict inequality

@gbswann 9 месяцев назад

Thanks!

@pankajsinha4280 3 года назад

Very good narrattive.

@hubert6943 3 года назад

is there any further reading to this topic?

@rounaksinha5309 3 года назад

Hii sir, I have a question, Is the relation differentiable like functions. If it is not then why do we differentiate the equation of circle to find the slope of tangent to it at a particular point despite of the fact that the equation of circle is not a function, as it fails the vertical line test.

@matekon2 3 года назад

Thank you

@ulysses_grant 3 года назад

Picasso: "I like it!" (about 11:28)

@sapientum8 3 года назад

good content

@djidelmaroua 2 года назад

Thank you so much!!! i really appreciate your efforts it really helped me to understand, best explanation ever

@goodplacetostop2973 3 года назад

13:40 Homework 13:47 Good Place To Stop

@random-td7tf 3 года назад

Can you link any other video which is unlisted ?

@dishonesttAbe 3 года назад

but if you require x,y,z to be unique integers, then "not equal to" is a transitive relation.

@user-wp1uw8fv6y 3 года назад

If we define "x is approximately equal to y (x ≒ y)" as "100/101 ≤ x/y ≤ 101/100" for positive real numbers x and y, then ≒ is symmetric, reflexive but not transitive.